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SciCode / 38.3 / Given some input vectors (could be one, two or three in total), provide the…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
step background
Background
For 1D case, the reciprocal vector is calculated as
$$
\begin{gathered}
\overrightarrow{a_1}=a \vec{x} \\
\overrightarrow{b_1}=\frac{2 \pi}{a_1} \vec{x}
\end{gathered}
$$
For 2D case,
$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$
where is a vector that is perpendicular to the 2D plane.
For 3D case, the function has been given.Plain-text mathematical notation (without MathML)
Background
For 1D case, the reciprocal vector is calculated as
$$
\begin{gathered}
\overrightarrow{a_1}=a \vec{x} \\
\overrightarrow{b_1}=\frac{2 \pi}{a_1} \vec{x}
\end{gathered}
$$
For 2D case,
$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$
where (a₃)→ is a vector that is perpendicular to the 2D plane.
For 3D case, the function has been given.Original LaTeX notation
Background
For 1D case, the reciprocal vector is calculated as
$$
\begin{gathered}
\overrightarrow{a_1}=a \vec{x} \\
\overrightarrow{b_1}=\frac{2 \pi}{a_1} \vec{x}
\end{gathered}
$$
For 2D case,
$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$
where $\overrightarrow{a_3}$ is a vector that is perpendicular to the 2D plane.
For 3D case, the function has been given.step description prompt
Given some input vectors (could be one, two or three in total), provide the reciprocal vectors. The input should be numpy array(s), and the output should be a list of one numpy array or some numpy arrays if there are more than one vectors.
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initial import